In a variety of contexts, observations are made of the outputs of an unknown multiple-input multiple-output linear system, from which it is of interest to recover the input signals. For example, in problems of enhancing speech in the presence of background noise, or separating competing speakers, multiple microphone measurements will typically have components from both sources with the linear system representing the effect of the acoustic environment.
Considering specifically the two-channel case, it is desired to estimate the two source signals s.sub.1 and s.sub.2, from the observation of the two output signals y.sub.1 and y.sub.2. In many applications one of the signals, s.sub.1, is the desired signal, while the other signal, s.sub.2, is the interference or noise signal. Both desired and noise signals are coupled through the unknown system to form the observed signals.
The most widely used approach to noise cancellation, in the two channel case, was suggested by Widrow et al. in "Adaptive Noise Canceling: Principles and Applications", Proc. IEEE, 63:1692-1716, which was published in 1975. In this approach, it is assumed that one of the observed signals, y.sub.1 --the primary signal, contains both the desired signal and an uncorrelated interfering signal, while the other observed signal, y.sub.2 --the reference signal, contains only the interference. The system that coupled the reference signal into the primary signal is found using the least mean square (LMS) algorithm. Then, the reference signal is filtered by the estimated system and subtracted from the primary signal to yield an estimate of the desired signal, s.sub.1. For example, U.S. Pat. No. 4,473,906 issued to Warnaka et al. used Widrow's approach and assumptions in an acoustic cancellation structure.
The main drawback of Widrow's approach lies in the crucial assumption that the reference signal is uncorrelated with the primary signal. This assumption is not realized in practice due to leakage of the primary signal into the reference signal. This degrades the performance of Widrow's method. Depending on the leakage (or cross-talk) power, this degradation may be severe, leading to a reverberant quality in the reconstructed signal since a portion of the desired signal is also subtracted, out of phase, together with the interference signal. Thus, a method of reconstruction is needed that can operate without making the unrealistic no-leakage assumption.